The availability of genomes of many closely related bacteria with diverse metabolic capabilities offers the possibility of tracing metabolic evolution on a phylogeny relating the genomes to understand the evolutionary processes and constraints that affect the evolution of metabolic networks. Using simple (independent loss/gain of reactions) or complex (incorporating dependencies among reactions) stochastic models of metabolic evolution, it is possible to study how metabolic networks evolve over time. Here, we describe a model that takes the reaction neighborhood into account when modeling metabolic evolution. The model also allows estimation of the strength of the neighborhood effect during the course of evolution. We present Gibbs samplers for sampling networks at the internal node of a phylogeny and for estimating the parameters of evolution over a phylogeny without exploring the whole search space by iteratively sampling from the conditional distributions of the internal networks and parameters. The samplers are used to estimate the parameters of evolution of metabolic networks of bacteria in the genus Pseudomonas and to infer the metabolic networks of the ancestral pseudomonads. The results suggest that pathway maps that are conserved across the Pseudomonas phylogeny have a stronger neighborhood structure than those which have a variable distribution of reactions across the phylogeny, and that some Pseudomonas lineages are going through genome reduction resulting in the loss of a number of reactions from their metabolic networks.

MOTIVATION: Most current research in network evolution focuses on networks that follow a Duplication Attachment model where the network is only allowed to grow. The evolution of metabolic networks, however, is characterized by gain as well as loss of reactions. It would be desirable to have a biologically relevant model of network evolution that could be used to calculate the likelihood of homologous metabolic networks. RESULTS: We describe metabolic network evolution as a discrete space continuous time Markov process and introduce a neighbor-dependent model for the evolution of metabolic networks where the rates with which reactions are added or removed depend on the fraction of neighboring reactions present in the network. We also present a Gibbs sampler for estimating the parameters of evolution without exploring the whole search space by iteratively sampling from the conditional distributions of the paths and parameters. A Metropolis-Hastings algorithm for sampling paths between two networks and calculating the likelihood of evolution is also presented. The sampler is used to estimate the parameters of evolution of metabolic networks in the genus Pseudomonas. AVAILABILITY: An implementation of the Gibbs sampler in Java is available at http://www.stats.ox.ac.uk/ approximately mithani/networkGibbs/. SUPPLEMENTARY INFORMATION: Supplementary data are available at the Bioinformatics online.

Abstract Summary:We present a tool called Rahnuma for prediction and analysis of metabolic pathways and comparison of metabolic networks. Rahnuma represents metabolic networks as hypergraphs and computes all possible pathways between two or more metabolites. It provides an intuitive way to answer biological ques- tions focusing on differences between organisms or the evolution of different species by allowing pathway-based metabolic network comparisons at an organism as well as at a phylogenetic level. Availability: Rahnuma is available online at http://portal.stats.ox.ac.uk:8080/rahnuma/. Contact: [email protected] Supplementary information: Supplementary data are available at the Bioinformatics online.